7.09/2.65	YES
7.09/2.66	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
7.09/2.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.09/2.66	
7.09/2.66	
7.09/2.66	Termination of the given C Problem could be proven:
7.09/2.66	
7.09/2.66	(0) C Problem
7.09/2.66	(1) CToIRSProof [EQUIVALENT, 0 ms]
7.09/2.66	(2) IntTRS
7.09/2.66	(3) TerminationGraphProcessor [SOUND, 50 ms]
7.09/2.66	(4) IntTRS
7.09/2.66	(5) IntTRSCompressionProof [EQUIVALENT, 0 ms]
7.09/2.66	(6) IntTRS
7.09/2.66	(7) TerminationGraphProcessor [EQUIVALENT, 2 ms]
7.09/2.66	(8) IntTRS
7.09/2.66	(9) IntTRSCompressionProof [EQUIVALENT, 0 ms]
7.09/2.66	(10) IntTRS
7.09/2.66	(11) PolynomialOrderProcessor [EQUIVALENT, 6 ms]
7.09/2.66	(12) YES
7.09/2.66	
7.09/2.66	
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(0)
7.09/2.66	Obligation:
7.09/2.66	c file /export/starexec/sandbox/benchmark/theBenchmark.c
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(1) CToIRSProof (EQUIVALENT)
7.09/2.66	Parsed C Integer Program as IRS.
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(2)
7.09/2.66	Obligation:
7.09/2.66	Rules:
7.09/2.66	f1(x, y) -> f2(x_1, y) :|: TRUE
7.09/2.66	f2(x1, x2) -> f3(x1, 23) :|: TRUE
7.09/2.66	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - x4
7.09/2.66	f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = x14 + 1
7.09/2.66	f3(x7, x8) -> f4(x7, x8) :|: x7 >= 0
7.09/2.66	f6(x9, x10) -> f3(x9, x10) :|: TRUE
7.09/2.66	f3(x11, x12) -> f7(x11, x12) :|: x11 < 0
7.09/2.66	Start term: f1(x, y)
7.09/2.66	
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(3) TerminationGraphProcessor (SOUND)
7.09/2.66	Constructed the termination graph and obtained one non-trivial SCC.
7.09/2.66	
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(4)
7.09/2.66	Obligation:
7.09/2.66	Rules:
7.09/2.66	f3(x7, x8) -> f4(x7, x8) :|: x7 >= 0
7.09/2.66	f6(x9, x10) -> f3(x9, x10) :|: TRUE
7.09/2.66	f5(x13, x14) -> f6(x13, x15) :|: TRUE && x15 = x14 + 1
7.09/2.66	f4(x3, x4) -> f5(arith, x4) :|: TRUE && arith = x3 - x4
7.09/2.66	
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(5) IntTRSCompressionProof (EQUIVALENT)
7.09/2.66	Compressed rules.
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(6)
7.09/2.66	Obligation:
7.09/2.66	Rules:
7.09/2.66	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > -1
7.09/2.66	
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(7) TerminationGraphProcessor (EQUIVALENT)
7.09/2.66	Constructed the termination graph and obtained one non-trivial SCC.
7.09/2.66	
7.09/2.66	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > -1
7.09/2.66	has been transformed into
7.09/2.66	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > -1 && x4 > -1.
7.09/2.66	
7.09/2.66	
7.09/2.66	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > -1 && x4 > -1 and 
7.09/2.66	f5(x13:0, x14:0) -> f5(x13:0 - (x14:0 + 1), x14:0 + 1) :|: x13:0 > -1 && x4 > -1
7.09/2.66	have been merged into the new rule
7.09/2.66	f5(x12, x13) -> f5(x12 - (x13 + 1) - (x13 + 1 + 1), x13 + 1 + 1) :|: x12 > -1 && x14 > -1 && (x12 - (x13 + 1) > -1 && x15 > -1)
7.09/2.66	
7.09/2.66	
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(8)
7.09/2.66	Obligation:
7.09/2.66	Rules:
7.09/2.66	f5(x16, x17) -> f5(x16 + -2 * x17 + -3, x17 + 2) :|: TRUE && x16 >= 0 && x18 >= 0 && x16 + -1 * x17 >= 1 && x19 >= 0
7.09/2.66	
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(9) IntTRSCompressionProof (EQUIVALENT)
7.09/2.66	Compressed rules.
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(10)
7.09/2.66	Obligation:
7.09/2.66	Rules:
7.09/2.66	f5(x16:0, x17:0) -> f5(x16:0 + -2 * x17:0 - 3, x17:0 + 2) :|: x16:0 + -1 * x17:0 >= 1 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1
7.09/2.66	
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(11) PolynomialOrderProcessor (EQUIVALENT)
7.09/2.66	Found the following polynomial interpretation:
7.09/2.66	[f5(x, x1)] = -1 + 2*x + x1^2
7.09/2.66	
7.09/2.66	The following rules are decreasing:
7.09/2.66	f5(x16:0, x17:0) -> f5(x16:0 + -2 * x17:0 - 3, x17:0 + 2) :|: x16:0 + -1 * x17:0 >= 1 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1
7.09/2.66	The following rules are bounded:
7.09/2.66	f5(x16:0, x17:0) -> f5(x16:0 + -2 * x17:0 - 3, x17:0 + 2) :|: x16:0 + -1 * x17:0 >= 1 && x19:0 > -1 && x16:0 > -1 && x18:0 > -1
7.09/2.66	
7.09/2.66	----------------------------------------
7.09/2.66	
7.09/2.66	(12)
7.09/2.66	YES
7.09/2.70	EOF